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AP EAMCET201823 Apr 2018Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

In A B C , if 3 A+ 3 B+ 3 C+ 3 =0 , then the least value of the sum of two of its angles is

Options

  1. A6
  2. B2 3
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

In a A B C , it is given that gathered 3 A+ 3 B+ 3 C+ 3 =0 2 3(A+B) 2 3(A-B) 2 + 3 C-1=0 -2 ( 3 C 2 ) 3(A-B) 2 +1-2 ^2 ( 3 C 2 )-1=0 3 C 2 [ 3(A-B) 2 - 3(A+B) 2 ]=0 3 A 2 3 B 2 3 C 2 =0 Means either A= 2 3 or B= 2 3 or C= 2 3 gathered So, the least value of the sum of two of its angles is - 2 3 = 3

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